Mackay's position at Cardiff City Stadium has been under scrutiny since the club decided to remove Iain Moody from his role as head of recruitment and replace him with 23-year-old Kazakhstani Alisher Apsalyamov on an interim basis.
Apsalyamov is thought to be a friend of Cardiff owner Vincent Tan's son and appears to have no previous experience in football.
Mackay attended a meeting of the club's board on Monday, where chief executive Simon Lim was expected to be present but not Tan, and the issue was almost certain to be high on the agenda.
It had been understood that Mackay had no intention of quitting the Bluebirds and his agent Raymond Sparkes, when asked if his client could resign, told BBC Radio Wales: "No, absolutely categorically not.
"Even now that's not something Malky is contemplating.
"There is absolutely no prospect of Malky resigning from a job that he loves, a job he's ensconced in."
Source: PA
Source: PA